Rewrite as a simplified fraction. ${3.6\overline{13} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3613.1313...\\ 10x &= 36.1313...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3577}$ ${x = \dfrac{3577}{990}} \text{or} {3 \dfrac{607}{990}}$